A physically-based moving boundary model of deltaic progradation is developed. Surface of the axially symmetric, inner delta is free to grow or shrink in time, while the sediment source is allowed to migrate along the streamwise direction. Particularly, the model developed here captures the control of a downstream migrating sediment source on a lateral extent of the delta. Along this line, the modelling results provide insight into the sedimentation processes associated with elongated fan–delta systems. Further calculations allow to determining the influence of ratio between water and sediment discharges on delta morphology. The model uses appropriately the laboratory observations described in a companion paper.